By Rao S. Govindaraju
This booklet bargains with the idea that of moments, and the way they locate software in subsurface hydrologic problems-particularly these facing solute shipping. either temporal and spatial moments are handled in a few element for a large choice of difficulties. numerous examples utilizing experimental information, either from laboratory columns and box experiments, are supplied to offer the readers a transparent thought concerning the scope of this system.
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Extra resources for Moment Analysis for Subsurface Hydrologic Applications (Water Science and Technology Library)
Sample text
In this section, we merely examine the various mathematical solutions to different boundary conditions. Consider the soil column to be of length L along the direction of average water movement. Specification of any particular boundary condition at the outlet x = L for solute movement is difficult. It is customary to mathematically impose the boundary condition at x = , and examine the solution at x = L. The evaluation of c L t in this manner allows solute efflux by both advection and dispersion mechanisms.
To accommodate this, the integral is computed over a semicircle, with the straight portion coincident with the infinite straight line. Letting the radius tend to infinite, the desired result is obtained by making the line integral along the arc of the semi-circle to vanish. 1. 2. Closing line integrals. (a) For t < 0; (b) For t > 0 we want est to vanish as the radius of the semi-circle approaches infinity. 2. 10) As mentioned earlier, it is required that f t = 0 for t < 0. 2), and account for all the singularities.
9) X CHAPTER 2 LAPLACE TRANSFORMS FOR SOLUTE TRANSPORT MODELS Transform methods are useful for solving linear partial differential equations. The choice of the appropriate transform depends on the kinds of boundary conditions and whether the domain is finite, infinite or semi-infinite. This chapter deals with the use of Laplace transforms, with emphasis on their role in solving partial differential equations that frequently arise in models of solute transport. 4, Laplace transforms were introduced as moment generating functions of continuous random variables.